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Questions tagged [optimization]

Optimization is the process of choosing the "best" value among possible values. They are often formulated as questions on the minimization/maximization of functions, with or without constraints.

In mathematics, computer science, economics, or management science, mathematical optimization (alternatively, optimization or mathematical programming) is the selection of a best element (with regard to some criteria) from some set of available alternatives.

An optimization problem can be represented in the following way: given a function $f:A\to\mathbb{R}$ from some set $A$ to the real numbers, we want to find an element $x_0\in A$ such that $f(x_0)\le f(x)$ for all $x \in A$ ("minimization") or such that $f(x_0)\ge f(x)$ for all $x \in A$ ("maximization").

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how to solve a minimization problem when a variable is complex, and an objective function is real?

Thank you for your help. I'd like to solve an optimization problem, with real-valued objective function and complex-valued control variable for example, my minimization problem is minimize conj(f(x))*f(x) with respect to x (x is a complex…
J.Kim
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formulate the single minisum facility location problem with the Chebyshev distance and linearize it.

Formulate the single minisum facility location problem with the Chebyshev distance and linearize it. Minisum rectilinear distance function is in here And Chebyshev is in here I couldn't figure out how to combine formulas. Thank you.
Bilge
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Choose the right optimization algorithm

I'd like to know how to choose a good optimization method for one problem. I know that it depends of the search space (mainly smoothness and modality). The issue is that you need to explore and observe this search space. That is to say, you need to…
Olstrom
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In active-set method, why only one constraint is deleted from working set at one time?

In the active-set optimisation method (especially quadratic programming), when we found multiple Lagrangian multipliers are negative at the stationary point, why couldn't we delete all of the corresponding constraints rather than deleting just one…
user112758
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minimizing sum of functions

Sorry in advance if this question is very simple for some. I need to minimize the sum of positive 2-D functions: $\sum_{i=1}^{N} f_i(k_0,k_1)$, and say that the values that optimize each of these functions are known, i.e., $k_{0,i}, k_{1,i}$. Is…
Yaz
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Checking if a set is bounded

While proving boundedness, how did we reach the maximum limits of x2 and x3 in A (the last line)?
LUCIFER
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What Optimization Algorithm/Technique Should I Use to Solve This Problem?

I am facing an optimization problem stated below: Find the values of $x_i$ where $i = 1, ..., 20$ and $0 \leq x_i \leq 1 $, to maximize $y$: $$y = \sum_{i = 1}^{20}\theta(1 - \theta)^{20 - i}(\alpha x_i + \beta(1 - x_i))$$ where $\theta \in (0, 1)$…
hklel
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Why are saddle point problems inherently harder than optimization problems for iterative methods?

The classical example is a saddle point of the function $$f: \mathbb R^2 \to \mathbb R, \\ \min_x \max_y f(x, y) = \min_x \max_y xy$$ If one applies "gradient decent" to this problem, i.e. follows $g(x, y) = (-x, y)$, then the method would get…
Ben Usman
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The better statistic to this case

I have two functions, say $f(x)$ and $g(x)$, being the first the 'observed' and the second the 'theoretical', which can be variable. What I aim to find is the $g(x)$ that best approximates to $f(x)$. Both functions are discrete, and I have 14 points…
cwasdwa
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Maximization with inequality constraints

I have to solve this optimization problem $$\underset{x}{\max} \left(AB-\frac{xC}{D}(E+F)\right)$$ subject to $$ \frac{AB}{x}-\frac{C}{D}(E+F) \leq G $$ and $$0 < x \leq \frac{ABD}{C(E+F)}. $$ How can I solve it?
user7341333
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Term by term minimization of a sum

I have a very basic level in optimization, so sorry in advance if my question is naive or very basic. I am considering an objective function $f(x_1, x_2, x_3) = \phi(x_1, x_2) + \psi(x_2, x_3)$ and I'm trying to minimize it over the variable $x =…
PAM
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maximization of a function

I am very new to optimization andI have to solve this equation max U(k)=tlog(1+ yhpg/(pg+s))+mpge^(-ky)) st k>0 can anyybody give me idea where should I start
user7341333
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Name of this optimization strategy?

Inspired by the approach of this paper and our own experiments, we optimize a complicated function as follows: 1. Get an initial estimate 2. Generate M perturbed variants of the inital estimate by adding noise 3. Evaluate the cost of all M starting…
BayerSe
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L1 Minimization with Non-negativity constraints.

Is there any fast approach to solving l1 minimization problem with non-negativity contraints? The problem is to minimize $|x_1|+|x_2|+...+|x_n|_{l_1}$ subject to $Ax = b$ and $Ax \geq 0$.
Strin
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optimize a piecewise defined function

I would like to optimize a function of the form $$u(x) = \begin{cases} \exp{(-\lambda x)} & \text{if } a \le x \le b \\ exp(-\lambda b) & \text{if } x > b \\ -\infty &\text{if } x< a\end{cases}$$ for some real constants $a,b$. I'm not very…
math
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